He is asking about issues concerning which the four imams differed

Praise
be to Allah.

Firstly: 

the points concerning which the four imams differed are many,
and it is not possible to comment on them in all topics of fiqh in an
article such as this answer, although it is possible to find out about them
from the books which deal with differences of opinion among the madhhabs,
such as al-Mughni by Ibn Qudaamah, Bidaayat al-Mujtahid by Ibn
Rushd, and similar books. 

But it is possible here to shed light on some of the reasons
for differences of opinion among the fuqaha’ in general terms. Some of the
reasons for their differences of opinion, for example, include the
following: 

1.    
Contradiction of
the shar‘ i evidence in the eyes of the mujtahid. 

The fuqaha’ differed in their methods of evaluating which
reports were more sound, or reconciling between different reports. The
scholars of the Standing Committee said, explaining the reasons for the
differences of opinion among the scholars: 

… Contradiction of the evidence: the fuqaha’ had different
points of view with regard to evaluating which reports were more sound, or
reconciling between different reports. For example, with regard to the
hadith which says that it is not allowed to offer any prayer after ‘Asr
until the sun has set, and the hadith which says that the one who enters the
mosque should not sit down until he offers two rak‘ahs to “greet the mosque”
(tahiyat al-masjid). The scholars differed concerning the application
of that to one who enters the mosque at a time when praying is disallowed.
Some of them gave precedence to the hadiths which say that praying at that
time is disallowed, and others gave precedence to the hadith about greeting
the mosque, and each side had evidence to support choosing which hadith
should be given precedence.

End quote from Fataawa al-Lajnah ad-Daa’imah, 1
(5/31) 

2.    
differences
related to the Arabic language, 

such as the difference of opinion regarding the
interpretation of words that may, linguistically, have two or more meanings,
such as the verse in which Allah, may He be exalted, says (interpretation of
the meaning): “And divorced women shall wait (as regards their marriage)
for three menstrual periods [quroo’]” [al-Baqarah 2:228]. The word quroo’
(translated here as “menstrual periods”), has two meanings; it may refer
linguistically to the end of the menses, whereupon the woman becomes pure,
or to the beginning of the menses. This text indicates that divorced women
should wait for three quroo’. It may be that what is meant is the end of the
third menses, or it may be that what is meant the beginning of the third
menses. This has been discussed previously in fatwa no. 170581. Ibn al-Qayyim
(may Allah have mercy on him) said in as-Sawaa’iq al-Mursalah
(2/565): 

For example, the differences that may arise as a result of
the word having more than one meaning, or being ambiguous, or something that
may be interpreted either according to the apparent meaning when used in
general terms, which is called the real meaning, or may be interpreted
according to the apparent meaning when used in specific terms, which is
called the metaphor, such as their difference of opinion as to what is meant
by quroo’: does it refer to the beginning or end of the menses? Some
understood it as referring to the beginning of menses and others understood
it as referring to the end of menses. End quote. 

3.    
Differences of
opinion concerning evidence that is general and whether it is valid or not 

For example: the deeds of the people of Madinah, as
transmitted through reports. Imam Maalik (may Allah have mercy on him) paid
a great deal of attention to the deeds of the people of Madinah, and he
thought that their deeds constituted valid proof regarding the religion of
Allah, may He be exalted, and that it was not permissible to go against
their consensus. This has been discussed previously in fatwa no.
179514. 

4.    
Differences due to
varying levels of knowledge and understanding of shar‘i texts 

The scholars of the Standing Committee said: As for the
reasons for differences of opinion among the scholars, there are many, such
as the fact that none of them had complete knowledge of everything, hence a
scholar may be unaware of something of which others are aware, and he may
understand from a text something that others do not understand from it, when
he is not aware of any unambiguous proof.

End quote from Fataawa al-Lajnah ad-Daa’imah 1
(2/178) 

5.    
Differences due to
the Sunnah (i.e., evaluation of hadith)

Such as the difference of opinion as to whether a hadith is
saheeh (sound) or da‘eef (weak). Ibn al-Qayyim (may Allah have mercy on him)
said in as-Sawaa‘iq al-Mursalah fi’r-Radd ‘ala al-Jahamiyyah
wa’l-Mu‘attilah (2/556), when explaining the reasons for the differences
of opinion: 

…The third reason: belief that a hadith is da‘eef at a time
when others may have a different view of that hadith based on their own
examination of it. So one of the scholars may think that a narrator is
da‘eef (weak) and not to be trusted, whilst another thinks that he is
trustworthy and qawiy (strong). The correct view may be that of the one who
regards the narrator as da‘eef, because he is aware of a reason of which the
one who regards the narrator as trustworthy was unaware. Or the correct view
may be that of the other one because he knows that that reason does not
undermine the reports or good character of that narrator. End quote. 

Or some of them may stipulate some conditions for aahaad
reports that were not stipulated by others. Ibn al-Qayyim (may Allah have
mercy on him) said in as-Sawaa‘iq al-Mursalah (2/559):

… The fourth reason: stipulation by some of them of
conditions with regard to aahaad reports that differ from those stipulated
by others. For example, some of them stipulated that the narrator should be
a faqeeh, if he narrates something that is contrary to analogy; some of them
stipulated that the hadith should be widely narrated and known if it
discusses an issue that is widespread among the people; some of them
stipulated that the hadith should not include any addition to the text of
the Qur’an, lest that lead to abrogation of a Qur’anic text as a result. 

6.    
Differences with
regard to usooli principles 

Such as their difference of opinion with regard to what is
meant by a specific text: is it to be understood according to the general
meaning of the text or is it made specific by a later text? Such as their
difference of opinion regarding texts that speak of commands and
prohibitions (and the degree of obligation or prohibition), and their
difference of opinion with regard to the apparent meaning of the wording and
how it is to be understood, and so on. 

For more information, please see the answer to question no.
128658 

Secondly: 

With regard to the issue of following a specific madhhab
among the four, this has been discussed in detail, quoting the opinions of
the scholars, in fatwas no. 21420 and
103339. Please see also fatwa no.
148057 for the ruling on following a madhhab. 

And Allah knows best.